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BGonline.org Forums
OLM 20140401A -- The Dilly Builders
Posted By: kruidenbuiltje In Response To: OLM 20140401A -- The Dilly Builders (Jason Lee)
Date: Friday, 4 April 2014, at 5:04 p.m.
Since blue is far ahead in the race playing safe would be my idea.
Blue is ahead 50 pips after this move (13/8 14/8), so he can try a few times before his advantage is wasted
Can we estimate the chance that blue can cross the enemy field?
a) White will hit and cover with (D1,21,31,41,D3,D4) = 9/36
b) White will have double coverage of the outfield with (51,61,D2,32,42,52,62,43,53,63,54,65,D6) = 24/36
c) White will have single coverage with (64,D5) = 3/36
a) D3 is killing, but after the other moves blue has on average about 4/36 escape routes to the outfield, of which he will on average survive 2/3. This group will produce almost 1 win for blue.
b) Blue will have to throw a 5 or 6, but if he does he will survive about 1/3 of the time. So this group will give blue about 4 wins.
c) This group will produce about 1 win for blue.
So, on his first outbreak-try blue will win about 6 out of 36 times, each time it doesn't work he will lose about 10 pips.
Thus he can try it 5 times before his advantage has dissipated. Each following time escaping will get harder. Let's make a sequence for it: for example 6+4+3+2+1 = 16 out of 36.
The sequence also makes it clear that white will have a double/take situation after the first attempt has failed.
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After 21/15 13/8 white will hit 26/36 times, only {23,D2,D3,34,35,24,25} = 12/36 will hit and cover. In the no-cover-situations blue has a lot of returns. On average about 14/36. So effectively white only hits 21/36 of the time. After the hit and covers (for example after 24 blue has a return {43,25,16,D1,13,21,23,41} = 15/36) the returns vary from 5/36 to 15/36, say on average 10/36. This reduces the effective hits even further to about 18/36.
So already in the first breakout try blue will have 18 out of 36 (effective) non-hits. I guess blue will safety his checkers half the time, that's already 9 out of 36 in the first try. The funny thing is that the second try in this case will not get much harder, since in a lot of cases the outfield control of white is diminished.
If I try to make a sequence of the second situation it would be something like 9+8+6 + .. = 23 + ... out of 36.
In conclusion: 21/15 13/8 is a lot better because it puts more pressure on the white midpoint.
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